Analysis of the FASSSTrotational spectrum of NCNCS in view of quantum monodromy

Abstract

Quantum monodromy has a strong impact on the ro-vibrational energy levels of chain molecules whose bending potential energy function has the form of the bottom of a champagne bottle (i.e. with a hump or punt) around the linear configuration. NCNCS, cyanogen iso-thiocyanate, is a particularly good example of such a molecule and clearly exhibits a distinctive monodromy-induced dislocation of the energy level pattern at the bending-rotation energy at the top of the potential energy hump. Indeed, NCNCS [B. P. Winnewisser et al., Phys. Rev. Lett. 2005, 95, 243002] and the water molecule [N. F. Zobov et al., Chem. Phys. Lett. 2005, 414, 193–197] were the first two molecules for which experimental confirmation of quantum monodromy was obtained. We used the fast scan sub-millimetre spectroscopic technique (FASSST) to extend the measurements and spectral analysis to pure rotational transitions (end-over-end) in bending vibrational states lying well above the monodromy point. The analysis of 9204 lines assigned to 7 vibrational states, presented here, shows that the topological properties of the bending potential function are mapped onto every aspect of the ro-vibrational energy levels involving excitation of the quasi-linear bending vibration. In order to model the large amplitude dynamics of such a molecular system, and also to achieve some insight beyond satisfactory parameters for reproducing the spectrum, we used the generalized semi-rigid bender (GSRB) Hamiltonian, which is described in some detail. This Hamiltonian provides a good description of the energy levels over the seven bending states observed, coming close to experimental accuracy. Due to high J values of the measured rotational transitions (J ≤ 116), the least squares fitting procedure was applied not directly to the measured frequencies, but to effective constants derived from fitting the transition frequencies to a set of polynomials in J(J + 1) yielding effective B_eff and D_eff constants. The GSRB wave functions are used to show that the expectation values of any quantity which varies with the large amplitude bending coordinate will also have monodromy-induced dislocations. This includes the electric dipole moment components. High level ab initio calculations not only provided the molecular equilibrium structure of NCNCS, but also the electric dipole moment components μ_a and μ_b as functions of the large-amplitude bending coordinate. Calculated expectation values of these quantities for individual ro-vibrational levels show the now recognizable monodromy pattern. Finally, a generalization of the quasi-linear parameter γ₀ is suggested.